How to round a plane to a sphere surface
I guess the easiest way is to extrude and bevel. You can tweak the shape in the Operator box, or scale later on the Z axis:


You can also customize the profile of the bevel in the Operator box:

To illustrate John Eason solution, you can inset your top face (i):

Then bevel (CtrlB) to create additional edges:

Enable Proportional Editing (Sphere mode) and move up the central face:

Tweak the parameters in the Operator box if necessary: